Pretend you have the following data for 16 subjects in a study designed to determine whether strong coffee speeds neural processing, in this case defined as reaction time in a simple memory task, with lower numbers reflecting faster processing. The 16 subjects were randomly assigned to two groups: placebo control group vs. coffee experimental group. Here are the results, followed by guidance for the VassarStats program: Placebo Coffee 28 26 23 18 20 15 28 24 29 24 33 19 34 13 http://vassarstats.net/ #1. What is the null hypothesis for this study? #2. a. State the mean for each group: Placebo mean = ?? Coffee mean = ?? b. What is the mean difference? #3. a. What was the level of significance (two-tailed p value)? b. What, then, is the probability that “chance” explained this mean difference given that p value? #4. a. What is your decision regarding the null hypothesis given the p value? Accept or reject? b. Are the results “significant” or “not significant?” #5. What is your overall conclusion given your statistical findings?

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Description: Pretend you have the following data for 16 subjects in a study designed to determine whether strong coffee speeds neural processing, in this case defined as reaction time in a simple memory task, with lower numbers reflecting faster processing. The 1

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Pretend you have the following data for 16 subjects in a study designed to determine whether strong coffee speeds neural processing, in this case defined as reaction time in a simple memory task, with lower numbers reflecting faster processing. The 16 subjects were randomly assigned to two groups: placebo control group vs. coffee experimental group.

Here are the results, followed by guidance for the VassarStats program:

Placebo Coffee

28 26

23 18

20 15

28 24

29 24

33 19

34 13

http://vassarstats.net/

#1. What is the null hypothesis for this study?

#2.

a. State the mean for each group: Placebo mean = ?? Coffee mean = ??

b. What is the mean difference?

#3.

a. What was the level of significance (two-tailed p value)?

b. What, then, is the probability that “chance” explained this mean difference given that p value?

#4.

a. What is your decision regarding the null hypothesis given the p value? Accept or reject?

b. Are the results “significant” or “not significant?”

#5. What is your overall conclusion given your statistical findings?

17 13

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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